6 Different US Coins are dated 1801 so on your browser type in "1801 US coins" click images & search. You should be able to see what they look like.
1846 was the first year for an "O" mintmark on a dollar coin. Look at the coin again and post new question.
It's just a presidential dollar coin value is $1.00
The US coin looks very much like a modern US penny
The only US coin that has the dual-dates of 1797-1801 on the obverse is a 2007 John Adams Presidential dollar, the date and mintmark is on the edge of the coin. If you got the coin from a bank or change, it's face value. Only a proof or mint state coin will have a premium.
Look at the coin again. The first US one cent coin was struck in 1793.
1846 was the first year for an "O" mintmark on a dollar coin. Look at the coin again and post new question.
It's just a presidential dollar coin value is $1.00
The US coin looks very much like a modern US penny
The only US coin that has the dual-dates of 1797-1801 on the obverse is a 2007 John Adams Presidential dollar, the date and mintmark is on the edge of the coin. If you got the coin from a bank or change, it's face value. Only a proof or mint state coin will have a premium.
Look at the coin again. The first US one cent coin was struck in 1793.
About the width of a US penny (one cent coin)
A genuine 1801 Bust silver dollar is worth no less than $700 and possibly over $10,000 depending on condition. If by chance the coin is golden in color, with a picture of Thomas Jefferson and the dates 1801-1809 on it, then it's a modern presidential dollar, worth one dollar.
The US didn't mint any $1 gold coins in 1801. My guess is that you almost certainly have a modern presidential dollar coin. 1801 is the date of the start or end of that president's term - the minting date is on the coin's edge. And it's made of brass rather than gold so it's only worth $1. Feel free to spend it. Hundreds of millions are being minted.
The current US penny coin features the Union Shield Crest on the back side of the coin. A banner with the words one cent goes over the shield.
No such US coin exists. You might have one from a different country, but you'd have to specify which country you were talking about.
That depends on the denomination of coin.
It may have been plated with gold but it adds nothing to the value of the coin.